Breakdown of scaling in droplet fission at high Reynolds number

Physics of Fluids

Volumn 9, Issue 6, 1997, Pages 1573-1590

  Brenner, Michael P ^a   Eggers, Jens ^b   Joseph, Kathy ^c   Nagel, Sidney R ^c   Shi, X D ^c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF DUISBURG ESSEN   (Germany)

^c UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DROPLETS; INTERFACES-FLUID; SCALING;

EID: 0030766470     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869279     Document Type: Article

References (43)

1. J. Plateau, Statique Experimentale et Theoretique des Liquides Soumis ant Seales Force Moleculaire (Gauthier Villars, Paris, 1873).
2. W. S. Rayleigh, "On the instability of jets," Proc. London Math. Soc. 4, 10 (1878).
3. A. M. Worthington, A Study of Splashes (Longmans, London, 1908).
4. H. E. Edgerton, Stopping Time: The Photographs of Harold Edgerton (Abrams, New York, 1987).
5. E. A. Hauser, H. E. Edgerton, and W. B. Tucker, "The application of the high-speed motion picture camera to the research on the surface tension of liquids," J. Phys. Chem. 40, 973 (1936).
6. H. E. Edgerton, E. A. Hauser, and W. B. Tucker, "Studies in drop formation as revealed by the high-speed motion camera," J. Phys. Chem. 41, 1017 (1941).
7. R. J. Donnelly and W. Glaberson, "Experiments on the capillary instability of a liquid jet," Proc. R. Soc. London Ser. A 290, 547 (1996).
8. E. F. Goedde and M. C. Yuen, "Experiments on liquid jet instability," J. Fluid Mech. 40, 495 (1970).
9. D. F. Rutland and G. J. Jameson, "A nonlinear effect in the capillary instability of liquid jets," J. Fluid Mech. 46, 267 (1971).
10. K. C. Chaudhary and T. Maxworthy, "The nonlinear capillary instability of a liquid jet. Part 2: Experiments in jet behavior before droplet formation," J. Fluid Mech. 96, 275 (1980).
11. K. C. Chaudhary and T. Maxworthy, "The nonlinear capillary instability of a liquid jet. Part 3: Experiments on satellite drop formation and control," J. Fluid Mech. 96, 287 (1980).
12. N. N. Mansour and T. S. Lundgren, "Satellite formation in capillary jet breakup," Phys. Fluids A 2, 114 (1990).
13. H. A. Stone, B. J. Bentley, and I. G. Leal, "An experimental study of transient effects in the breakup of viscous drops," J. Fluid Mech. 173, 131 (1986).
14. H. A. Stone and L. G. Leal, "Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid," J. Fluid Mech. 198, 399 (1989).
15. M. Tjahjadi, H. A. Stone, and J. M. Ottino, "Satellite and subsatellite formation in capillary breakup," J. Fluid Mech. 243, 297 (1992).
16. P. Constantin, T. Dupont, R. Goldstein, L. Kadanoff, M. Shelley, and S. Zhou, "Droplet breakup in the Hele-Shaw cell?." Phys. Rev. E 47, 4169 (1993).
17. T. Dupont, R. Goldstein, L. Kadanoff, and S. Zhou, "Finite-time singularity formation in Hele-Shaw systems," Phys. Rev. E 47, 4182 (1993).
18. R. E. Goldstein, A. I. Pesci, and M. J. Shelly, "Topology transitions and singularities in viscous flows," Phys. Rev. Lett. 70, 3043 (1993).
19. A. Bertozzi, M. Brenner, T. Dupont, and L. Kadanoff, "Singularities and similarities in interface flow," in Centennial Edition, Applied Mathematics Series edited by L. Sirovich (Springer-Verlag, Berlin, 1993).
20. D. H. Peregrine, G. Shoker, and A. Symon, "The bifurcation of liquid bridges," J. Fluid Mech. 212, 25 (1990).
21. J. Keller and M. J. Miksis, "Surface tension driven flows," SIAM J. Appl. Math. 43, 268 (1983).
22. G. I. Barenblatt, Similarity, Self-Similarity and Intermediate Asymptotics (Consultants Bureau, New York, 1979).
23. R. Almgren, A. Bertozzi, and M. P. Brenner "Stable and unstable singularities in the unforced Hele-Shaw cell," Phys. Fluids 8, 1 (1996).
24. J. Eggers and T. F. Dupont, "Drop formation in a one-dimensional approximation of the Navier-Stokes equation," J. Fluid Mech. 262, 205 (1994).
25. J. Eggers, "Universal pinching of 3d axisymmetric free-surface flow," Phys. Rev. Lett. 71, 3458 (1993).
26. J. Eggers, "Theory of drop formation," Phys. Fluids 7, 941 (1994).
27. X. D. Shi, M. P. Brenner, and S. R. Nagel, "Cascade of structue in a drop droplet fission," Phys. Rev. Lett. 73, 3391 (1994).
28. M. P. Brenner, X. D. Shi, and S. R. Nagel, "Iterated instabilites during droplet fission," Phys. Rev. Lett. 73, 3391 (1994).
29. J. B. Keller, "Breaking of liquid films and threads," Phys. Fluids 26, 3451 (1983).
30. S. Bechtel, M. G. Forest, and K. J. Lin, "Closure to all orders in 1d models for slender viscoelastic free jets: An integrated theory for axisymmetric, torsionless flows," Stability Appl. Anal. Continuous Media 2, 59 (1992).
31. R. W. Sellens, "A one-dimensional numerical model of the capillary instability," Atom Sprays 2, 236 (1992).
32. X. Zhang and O. A. Basaran, "An experimental study of dynamics of drop formation," Phys. Fluids 7, 1184 (1995).
33. H. C. Lee, "Drop formation in a liquid jet," IBM J. Res. Dev. 18, 364 (1974).
34. D. B. Bogy, "Drop formation in a circular liquid jet," Annu. Rev. Fluid Mech. 11, 207 (1979).
35. A. E. Green, "On the non-linear behavior of fluid jets," Int. J. Eng. Sci. 14, 49 (1976).
36. S. E. Gechtel, C. D. Carlson, and M. G. Forest, "Recovery of the Rayleigh capillary instability from slender 1-d inviscid and viscous models," Phys. Fluids 7, 2956 (1995).
37. R. M. S. M. Schulkes, "The evolution and bifurcation of a pendant drop," J. Fluid Mech. 278, 83 (1994).
38. T. Y. Hou, J. S. Lowengrub, and M. J. Shelley, "The long time motion of vortex sheets with surface tension," submitted to Phys. Fluids.
39. L. Ting and J. B. Keller, "Slender jets and thin sheets with surface tension," SIAM J. Appl. Math. 50, 153 (1990).
40. Y. J. Chen and P. H. Steen, "Dynamics of inviscid capillary breakup: Collapse and pinchoff of a film bridge," to appear in J. Fluid Mech.
41. W. van Saarloos, "Front propagation into unstable states: Marginal stability as a dynamical mechanism for velocity selection," Phys. Rev. A 37, 211 (1988).
42. T. W. Shield, D. B. Bogy, and F. E. Talke, "A numerical comparison of one dimensional fluid jet models applied to drop-on-demand printing," J. Comput. Phys. 67, 327 (1986).
43. J. B. Keller, A. King, and L. Ting, "Blob formation," Phys. Fluids 7, 226 (1995).